Studies of Euler diagrams/farofe

dummy This Boolean function has 12 of 16 true spots. It is similar to medusa, but without spot 3. (See here.)

The Euler diagrams shown above are not good, because they hide the symmetry of this Boolean function.

This code uses the Python library discrete helpers. from discretehelpers.boolf.examples import farofe assert farofe.symmetric_spots.blocks_with_singletons() == [[0, 4], [1, 5], [2, 12], [6, 8], [7, 9], [10, 14]]

Each of the 6 pairs is a 2-split (with all 4 quadrants). Only one of the 4 triples is a 3-split (with all 8 octants).

Euler diagram
4 sets A B C D 6 pairs A B A C A D C D B D B C 4 triples B C D 8 cells A C D 7 cells A B D 7 cells A B C 7 cells

graph
complete 4 sets A B C D 6 pairs A B A C A D C D B D B C 4 triples B C D A C D A B D A B C